Cryptology ePrint Archive: Report 2012/161

New Constructions of Low Correlation Sequences with High Linear Complexity

Hai Xiong, Chao Li, Qingping Dai, Shaojing Fu

Abstract: In this paper, we propose a new concept named similar-bent function and we present two general methods to construct balanced sequences with low correlation by using similar-bent functions and orthogonal similar-bent functions. We nd that the bent sequence sets are special
cases of our construction. We also investigate the linear complexity of the new constructed sequences. If a suitable similar-bent function is given, the sequences constructed by it can have high linear complexity. As examples, we construct two new low correlation sequence sets. One constructed based on Dobbertin's iterative function is asymptotically optimal with respect to
Welch's bound and the other one is constructed based on Kasami function whose sequences have a high linear complexity.